In transmitters in wireless communications systems, such as the transmitters in the base stations of cellular access systems, it is a desire to keep the power consumption low and to maintain energy efficient communication with the users in the cell or cells that is/are serviced by the base station. There are a number of reasons for this, among which the following can be mentioned:                An operator who can reduce the power/energy consumption will become more cost-efficient, and thus yield increased revenue. The energy cost is generally considered to be a substantial part of the Operating cost.        An operator may also be interested in offering the best (or, for the service, sufficient) performance to his customers in relation to the power/energy that is invested.        Manufacturers are interested in reducing the power/energy consumption of base stations and other equipment, since that may lead to lower manufacturing costs due to fewer/smaller cooling components and power amplifiers, and will improve their competitiveness and sales margins due to lower manufacturing costs.        Reduced energy/power consumption is also beneficial for solar panel driven base stations as it enables prolonged operation and/or increased range given an energy/power budget. This is of particular interest when enabling cellular services to future users, who often live in rural areas with little or no infrastructure, such as an electricity grid.        An operator operating a system in remote areas which often lack distribution systems for electricity may often need to rely on fuel, e.g. often diesel, driven generators, and hence requires tedious and costly transport and management of this fuel. It would be desirable to reduce this problem by a more energy and power efficient design.        More resource-efficient methods for communication are also of interest for society as a whole, given the climate change problem, and acknowledging that the source of electricity for most cellular systems is often based on non-renewable fossil fuel.        
In addition, it is a generally good design philosophy to minimize energy consumption.
The so called “Water-filling” solution is a well known technique for power and rate allocation in a cellular wireless access system, when communicating over multiple carriers/channels with different gain to noise ratios, and provides the optimal performance, typically measured as the sum rate, for a given investment of sum power. The “water filling” solution provides power and rate allocation for each channel.
Consider a Gaussian vector channel with J orthogonal channels, each indexed with the letter j, where the noise-to-gain ratios qj=σj2/Gj are known for all channels, and where σj2 is the noise and interference power and Gj is the channel gain. The problem is to determine the channel power allocations Pj that maximizes the total (Shannon) rate over all channels subject to a constraint on total sum power P(tot):
      max    ⁢                  ∑                  ∀          j                    ⁢              R        j                        s      .      t      .                        ∑                      ∀            j                          ⁢                  P          j                      =          P              (        tot        )                        R      j        =                  log        2            ⁡              (                  1          +                                    P              j                        ⁢                                          G                j                            /                              σ                j                2                                                    )                        P      j        ≥    0  
The term “s.t.” in the equation above stands for “subject to”, and indicates the constraint under which the optimization is performed. In this case, the optimization is a maximization of the sum rate for each channel j. Rj stands for the maximum permissible communication rate. The rate here is synonymous with channel capacity in b/Hz/s.
Pj*,Rj * are the solutions to the above optimization problem according to
      P    j    *    =      {                                                                                        λ                  -                                                            σ                      j                      2                                        /                                          G                      j                                                                      ,                                                                                      if                  ⁢                                                                          ⁢                  λ                                >                                                      σ                    j                    2                                    /                                      G                    j                                                                                                                          0                ,                                                    Otherwise                                      ⁢                                  ⁢                  R          j          *                    =                        log          2                ⁡                  (                      1            +                                          P                j                *                            ⁢                                                G                  j                                /                                  σ                  j                  2                                                              )                    where λ is a so called Lagrange parameter which is tuned to fulfil the condition that all the transmit powers add up to a total power Ptot.
In wireless communications systems, such as cellular access systems, the transmitter, for example in a base station, generally has the task of assigning resources, such as channels and rates, for communication with users of the system, as well as assigning suitable power and rates.
Since a base station may communicate with multiple users, especially in multicarrier systems such as OFDMA systems exemplified by LTE (i.e. 3GPP's Long Term Evolution), IEEE 802.16 and others, the classical water-filling solution is interesting, but is insufficient since it does not address the existence of multiple users. Other examples of multi carrier systems are SC-FDMA systems. (SC-FDMA: Single Carrier Frequency Division Multiple Access).
Commonly in wireless access systems, channel assignment is treated separately from power and rate control, i.e. the system first selects channels, and then, independently, assigns power and rates. Moreover, while there are examples where power and rate are jointly adapted, it is common in practice that the system either roughly tries to use a fixed power level with adaptive rate (HSDPA in 3GPP's WCDMA) or fixed rate with adaptive power (DCH for WCDMA in 3GPP's WCDMA, or DCH in GSM).
Nevertheless, the problem of dealing with multiple users and assigning powers and rates simultaneously has been addressed in various forms. However, in general, existing solutions do not provide for a simple, and a flexible framework which is adaptive to different and/or changing power and rate constraints, both on a system and individual user level.